This discussion meeting is aimed at promoting fruitful interactions between theoretical physicists and mathematicians in areas that could be of common interest. In the past few decades, the interaction between algebraic geometry and quantum field theory has contributed substantial insights to both areas. Now seems to be an opportune moment to extend the areas of cross-fertilisation to include arithmetic geometry, comprising the study of arithmetic schemes and their Diophantine geometry, the theory of Galois representations, and the arithmetic Langlands programme.The ICTS discussion meeting will focus on some ideas that Minhyong Kim and others have been pursuing (see Link). There are analogies between the moduli spaces of arithmetic principal bundles and constructions in quantum field theory, in particular, Chern-Simons theory. The idea of the meeting is to have about a dozen number theorists and string theorists (and some other local participants) to explore this common ground. There ...
